Difference between revisions of "Quadratic form"
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== Description == | == Description == | ||
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| + | For example: | ||
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| + | 4x^2 + 2xy - 3y^2 | ||
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| + | is a quadratic form in the variables x and y. | ||
Quadratic forms occupy a central place in various branches of mathematics, including [[number theory]], [[linear algebra]], [[group theory]] ([[orthogonal group]]), [[differential geometry]] (Riemannian metric), [[differential topology]] (intersection forms of four-manifolds), and [[Lie theory]] (the [[Killing form]]). | Quadratic forms occupy a central place in various branches of mathematics, including [[number theory]], [[linear algebra]], [[group theory]] ([[orthogonal group]]), [[differential geometry]] (Riemannian metric), [[differential topology]] (intersection forms of four-manifolds), and [[Lie theory]] (the [[Killing form]]). | ||
Revision as of 22:27, 3 September 2016
In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.
Description
For example:
4x^2 + 2xy - 3y^2
is a quadratic form in the variables x and y.
Quadratic forms occupy a central place in various branches of mathematics, including number theory, linear algebra, group theory (orthogonal group), differential geometry (Riemannian metric), differential topology (intersection forms of four-manifolds), and Lie theory (the Killing form).
See also
- ε-quadratic form
- Quadratic form (statistics)
- Quadric
- Discriminant of a quadratic form
- Cubic form
- Witt group
- Witt's theorem
- Hasse–Minkowski theorem
- Orthogonal group
- Square class
- Ramanujan's ternary quadratic form
- Variable (mathematics)
External links
- Quadratic form @ Wikipedia.org
